%% Saturn
warning off
clc;clear;
format longg
options_negx = odeset('RelTol',1e-13,'AbsTol',1e-13,'Events',@NegXcrossing);
options=odeset('RelTol',1e-13,'AbsTol',1e-13);
options_fmincon = optimoptions('fmincon', 'MaxFunctionEvaluations', 5000, ...
    'MaxIterations', 5000,'ConstraintTolerance',1e-6,'Algorithm','Interior-point','stepTolerance',1e-21);
%% Inputs.
G           = 6.674e-11 * ((1/1000)^3); % Gravitational parameters

mass_central = 1.989e30;
%[] Mass of central planet

mass_moon = 5.972e24;         %Callisto
%[] mass of moons

DU = 151.73e6;           %Callisto
%[km] Semi-major axis of Moons, used as distance units for each CRTBP
%environment.

moonName = {'Luna'};
%[] Name of the Moons

thetao = 0;
%[] Initial position of the moon relative to the first point of aries

GM_central = mass_central*G;
%[] Gravitational parameters

GM_moon = mass_moon*G;
%[] Gravitational parameters

N = length(mass_moon);
%[] Number of Moons

u = zeros(N,1);
for ii = 1:N
    u(ii) = GM_moon(ii)/(GM_moon(ii)+GM_central);
end
%[] Gravataional ratio

TU = zeros(N,1);
VU = zeros(N,1);
for ii = 1:N
    TU(ii) = sqrt(DU(ii)^3/GM_central);
    VU(ii) = DU(ii)/TU(ii);
end
%[] Time constant for each crtbp system

theta_dot = zeros(1,N);
for ii = 1:length(theta_dot)
    theta_dot(ii) = sqrt(GM_central*DU(ii))/DU(ii)^2;
end
%[] Theta dot for each planet.

planetNumb = 1;
[L1,L2,L3,L4,L5] = librationPoints(u(planetNumb));
L_ = [L1,L2,L3,L4,L5];
for ii = 1:length(L_)
    L_pos = L_(:,ii);
    J_L(ii) = jacobiConst(L_pos,zeros(3,1),u(planetNumb));
end

%%



load('SE_L4_L5_Lyapunov.mat');

load('SE_L4_Vertical.mat');
ind = 1;
for ii = 1:10:length(T_L4_VL)
    Jacobi_Save_VL(ind) = jacobiConst(IC_L4_VL(1:3,ii),IC_L4_VL(4:6,ii),u);

    Xo_VL = IC_L4_VL(:,ii);
    to = [0:0.01:T_L4_VL(ii)];
    [~,S] = ode113(@(t,S)CR3BP_n(t,S,u),to,Xo_VL,options);
    S = S';
    COE_temp = zeros(size(S));
    for k = 1:length(S)

        COE_temp(:,k) = State2Coe(C2I_primary(S(:,k),u,DU,VU,0),GM_central);

    end

    SMA_VL_mean(ind) = mean(COE_temp(1,:))/DU;
    SMA_VL_std(ind) = std(COE_temp(1,:))/DU;
    e_VL_mean(ind) = mean(COE_temp(2,:));
    e_VL_std(ind) = std(COE_temp(2,:));
    i_VL_mean(ind) = mean(COE_temp(3,:));
    i_VL_std(ind) = std(COE_temp(3,:));
    clear COE_temp S 
    ind = ind +1;
end

%%
figure; hold on;
subplot(1,3,1);
plot(Jacobi_Save_VL,ones(1,length(Jacobi_Save_VL)),'k.','MarkerSize',11)
errorbar(Jacobi_Save_VL,ones(1,length(Jacobi_Save_VL)),SMA_VL_std,'LineStyle','none', 'Color', 'k','linewidth', 2)
xlabel('Jacobi''s Constant')
ylabel('Semi-major axis [DU]');
set(gca,'fontsize',14)

subplot(1,3,2);
plot(Jacobi_Save_VL,e_VL_mean,'k.','MarkerSize',11)
errorbar(Jacobi_Save_VL,e_VL_mean,e_VL_std,'LineStyle','none', 'Color', 'k','linewidth', 2)
xlabel('Jacobi''s Constant')
ylabel('Eccentricity');
set(gca,'fontsize',14)

subplot(1,3,3);
plot(Jacobi_Save_VL,i_VL_mean,'k.','MarkerSize',11)
errorbar(Jacobi_Save_VL,i_VL_mean,i_VL_std,'LineStyle','none', 'Color', 'k','linewidth', 2)
xlabel('Jacobi''s Constant')
ylabel('Inclination [deg]');
set(gca,'fontsize',14)
